Distinguishing wheel graphs by the alliance polynomial

2020/01/03 by Walter Carballosa, Omar Rosario, Carballosa, Walter +5
Mathematics · #05C69 #11B83 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05C69 #msc:11B83

paper · pdf · doi:10.48550/arxiv.2001.00990

This work was presented in the 49th Southeastern International Conference on Combinatorics, Graph Theory & Computing (CEICCGTC 2018)

arxiv created 2020/01/03 · arxiv updated 2020/01/07

Abstract

Distinctive power of the alliance polynomial has been studied in previous works, for instance, it has been proved that the empty, path, cycle, complete, complete without one edge and star graphs are characterized by its alliance polynomial. Moreover, it has been proved that the family of alliance polynomial of regular graphs with small degree is a very special one, since it does not contain alliance polynomial of graphs other than regular graph with the same degree. In this work we prove that the alliance polynomial also determines the wheel graphs.

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